The theorem says that v+f=e+2. This is taught in MA 375 and, in fancy terms, expresses the fact that the Euler characteristic of a 2-sphere equals 2. (More generally, Euler characteristics of even-dimensional spheres equal 2 and those of odd-dimensional spheres equal zero. This fact has the corollary that somewhere on earth the wind does not blow, and that you can't comb a hedgehog. No joke here...)
Find out what the Euler characteristic of a Klein bottle is by using the web!
